We use phpbb v. 3.03 for support. On our web site we have user registration page where user can elect to register for support in which case user is redirected to the phpbb registration page and after agreeing to the Terms navigates to the registration form.

We would like to avoid users having entering email address on phpbb registration form twice, since it is already entered on our web site registration page. Is there any solution that allows to include email address into the request to phpbb registration page so it will appear on the registration form in the first email field?

You might want to consider integrating the phpbb forum sessions into your existing website so users have a single login instead of having to re-register. I know it's not exactly what you asked but it seems like a better solution. Have a look at this article in the knowledgebase.